Physics > Popular Physics

Title:
Rowing and the Same-Sum Problem Have Their Moments

Abstract: We consider the optimal positioning of an even number of crew members in a
coxless racing boat in order to avoid the presence of a sideways wiggle as the
boat is propelled forwards through the water. We show that the traditional
(alternate port and starboard) rig of racing boats always possesses an
oscillating non-zero transverse moment and associated wiggling motion. We show
that the problem of finding the zero-moment rigs is related to a special case
of the Subset Sum problem. We find the one (known) zero-moment rig for a racing
Four and show there are four possible such rigs for a racing Eight, of which
only two (the so called 'Italian' and 'German' rigs) appear to be already
known. We also give the 29 zero-moment solutions for racing Twelves but refrain
from explicitly listing the 263 Sixteens and 2724 Twenties which have zero
transverse moments. We show that only balanced boats with crew numbers that are
divisible by four can have the zero-moment property. We also discuss some
aspects of unbalanced boats, in which the number of port and starboard oars are
unequal.